what you will learn module: module 55 firm...

What you will learn in this Module:

548 s e c t i o n 1 0 B e h i n d t h e S u p p l y C u r v e : P ro f i t , P ro d u c t i o n , a n d C o s t s

• The various types of cost

a firm faces, including fixed

cost, variable cost, and

total cost

• How a firm’s costs generate

marginal cost curves and

average cost curves

Module 55Firm Costs

From the Production Function to Cost Curves Now that we have learned about the firm’s production function, we can use thatknowledge to develop its cost curves. To see how a firm’s production function is relatedto its cost curves, let’s turn once again to George and Martha’s farm. Once George andMartha know their production function, they know the relationship between inputs oflabor and land and output of wheat. But if they want to maximize their profits, theyneed to translate this knowledge into information about the relationship between thequantity of output and cost. Let’s see how they can do this.

To translate information about a firm’s production function into informationabout its cost, we need to know how much the firm must pay for its inputs. We will as-sume that George and Martha face either an explicit or an implicit cost of $400 for theuse of the land. As we learned previously, it is irrelevant whether George and Marthamust rent the land for $400 from someone else or whether they own the land them-selves and forgo earning $400 from renting it to someone else. Either way, they pay anopportunity cost of $400 by using the land to grow wheat. Moreover, since the land is afixed input for which George and Martha pay $400 whether they grow one bushel ofwheat or one hundred, its cost is a fixed cost, denoted by FC—a cost that does not de-pend on the quantity of output produced. In business, a fixed cost is often referred toas an “overhead cost.”

We also assume that George and Martha must pay each worker $200. Using theirproduction function, George and Martha know that the number of workers they musthire depends on the amount of wheat they intend to produce. So the cost of labor,which is equal to the number of workers multiplied by $200, is a variable cost, de-noted by VC—a cost that depends on the quantity of output produced. Adding thefixed cost and the variable cost of a given quantity of output gives the total cost, or TC,of that quantity of output. We can express the relationship among fixed cost, variablecost, and total cost as an equation:

(55-1) Total cost = Fixed cost + Variable cost

or

TC = FC + VC

A fixed cost is a cost that does not depend

on the quantity of output produced. It is the

cost of the fixed input.

A variable cost is a cost that depends on

the quantity of output produced. It is the cost

of the variable input.

The total cost of producing a given quantity

of output is the sum of the fixed cost and

the variable cost of producing that quantity

of output.

The table in Figure 55.1 shows how total cost is calculated for George and Martha’sfarm. The second column shows the number of workers employed, L. The third columnshows the corresponding level of output, Q, taken from the table in Figure 54.1. Thefourth column shows the variable cost, VC, equal to the number of workers multipliedby $200. The fifth column shows the fixed cost, FC, which is $400 regardless of thequantity of wheat produced. The sixth column shows the total cost of output, TC,which is the variable cost plus the fixed cost.

The first column labels each row of the table with a letter, from A to I. These labelswill be helpful in understanding our next step: drawing the total cost curve, a curvethat shows how total cost depends on the quantity of output.

George and Martha’s total cost curve is shown in the diagram in Figure 55.1, wherethe horizontal axis measures the quantity of output in bushels of wheat and the verti-cal axis measures total cost in dollars. Each point on the curve corresponds to one rowof the table in Figure 55.1. For example, point A shows the situation when 0 workersare employed: output is 0, and total cost is equal to fixed cost, $400. Similarly, point Bshows the situation when 1 worker is employed: output is 19 bushels, and total cost is$600, equal to the sum of $400 in fixed cost and $200 in variable cost.

Like the total product curve, the total cost curve slopes upward: due to the in-creasing variable cost, the more output produced, the higher the farm’s total cost.

m o d u l e 5 5 F i r m C o s t s 549

f i g u r e 55.1

Total Cost Curve for Georgeand Martha’s FarmThe table shows the variable cost, fixed cost,and total cost for various output quantities onGeorge and Martha’s 10-acre farm. The totalcost curve shows how total cost (measured onthe vertical axis) depends on the quantity ofoutput (measured on the horizontal axis). Thelabeled points on the curve correspond to therows of the table. The total cost curve slopesupward because the number of workers em-ployed, and hence total cost, increases as thequantity of output increases. The curve getssteeper as output increases due to diminishingreturns to labor.

19 36 51 64 75 84 91 960

$2,000

1,800

1,600

1,400

1,200

1,000

800

600

400

200

Cost

Quantity of wheat (bushels)

AB

C

D

E

FG

Total cost, TC

H

I

ABCDEFGHI

Pointon graph

012345678

$400400400400400400400400400

O200400600800

1,0001,2001,4001,600

400600800

1,0001,2001,4001,6001,8002,000

Quantityof labor

L(workers)

01936516475849196

Quantityof wheat

Q(bushels)

VariablecostVC

FixedcostFC

Totalcost

TC = FC + VC

$ $

The total cost curve shows how total cost

depends on the quantity of output.


But unlike the total product curve, which gets flatter as employment rises, the totalcost curve gets steeper. That is, the slope of the total cost curve is greater as theamount of output produced increases. As we will soon see, the steepening of the totalcost curve is also due to diminishing returns to the variable input. Before we can seewhy, we must first look at the relationships among several useful measures of cost.

Two Key Concepts: Marginal Cost and

Average CostWe’ve just learned how to derive a firm’s total cost curve from its production function.Our next step is to take a deeper look at total cost by deriving two extremely usefulmeasures: marginal cost and average cost. As we’ll see, these two measures of the cost ofproduction have a somewhat surprising relationship to each other. Moreover, they willprove to be vitally important in later modules, where we will use them to analyze thefirm’s output decision and the market supply curve.

Marginal CostModule 53 explained that marginal cost is the added cost of doing something onemore time. In the context of production, marginal cost is the change in total cost gen-erated by producing one more unit of output. We’ve already seen that marginal prod-uct is easiest to calculate if data on output are available in increments of one unit ofinput. Similarly, marginal cost is easiest to calculate if data on total cost are available inincrements of one unit of output because the increase in total cost for each unit isclear. When the data come in less convenient increments, it’s still possible to calculatemarginal cost over each interval. But for the sake of simplicity, let’s work with an exam-ple in which the data come in convenient one-unit increments.

Selena’s Gourmet Salsas produces bottled salsa; Table 55.1 shows how its costs perday depend on the number of cases of salsa it produces per day. The firm has a fixed

Costs at Selena’s Gourmet Salsas

Quantity of salsa VariableQ Fixed cost cost Total cost

(cases) FC VC TC = FC + VC

t a b l e 55.1

$108

108

108

108

108

108

108

108

108

108

108

$108

120

156

216

300

408

540

696

876

1,080

$1,308

$0

12

48

108

192

300

432

588

768

972

1,200

0

1

2

3

4

5

6

7

8

9

10

Marginal cost of case

MC = ΔTC /ΔQ

$12

0036

0060

0084

108

132

156

180

204

228

cost of $108 per day, shown in the second column, which is the daily rental cost of itsfood-preparation equipment. The third column shows the variable cost, and the fourthcolumn shows the total cost. Panel (a) of Figure 55.2 plots the total cost curve. Like thetotal cost curve for George and Martha’s farm in Figure 55.1, this curve slopes upward,getting steeper as quantity increases.

The significance of the slope of the total cost curve is shown by the fifth column ofTable 55.1, which indicates marginal cost—the additional cost of each additional unit.The general formula for marginal cost is:

(55-2) Marginal cost = =

or

MC =

As in the case of marginal product, marginal cost is equal to “rise” (the in-crease in total cost) divided by “run” (the increase in the quantity of out-put). So just as marginal product is equal to the slope of the total productcurve, marginal cost is equal to the slope of the total cost curve.

Now we can understand why the total cost curve gets steeper as it in-creases from left to right: as you can see in Table 55.1, marginal cost atSelena’s Gourmet Salsas rises as output increases. And because mar-ginal cost equals the slope of the total cost curve, a higher marginal costmeans a steeper slope. Panel (b) of Figure 55.2 shows the marginal costcurve corresponding to the data in Table 55.1. Notice that, as in Figure53.1, we plot the marginal cost for increasing output from 0 to 1 case ofsalsa halfway between 0 and 1, the marginal cost for increasing outputfrom 1 to 2 cases of salsa halfway between 1 and 2, and so on.

ΔTCΔQ

Change in totalcost generated byone additional unitof output

Change in total costChange in quantity of output


$250

200

150

100

50

Costof case

Quantity of salsa (cases)7 8 9 106543210

$1,400

1,200

1,000

800

600

400

200

Cost


(b) Marginal Cost(a) Total Cost

TC MC

2nd case of salsa increases totalcost by $36.

8th case of salsa increases totalcost by $180.

Total Cost and Marginal Cost Curves for Selena’s Gourmet Salsasf i g u r e 55.2

Panel (a) shows the total cost curve from Table 55.1. Like the total costcurve in Figure 55.1, it slopes upward and gets steeper as we move up

it to the right. Panel (b) shows the marginal cost curve. It also slopesupward, reflecting diminishing returns to the variable input.

iSto

ckph

oto

Why does the marginal cost curve slope upward? Because there are diminishing re-turns to inputs in this example. As output increases, the marginal product of the vari-able input declines. This implies that more and more of the variable input must beused to produce each additional unit of output as the amount of output already pro-duced rises. And since each unit of the variable input must be paid for, the additionalcost per additional unit of output also rises.

Recall that the flattening of the total product curve is also due to diminishing re-turns: if the quantities of other inputs are fixed, the marginal product of an input fallsas more of that input is used. The flattening of the total product curve as output in-creases and the steepening of the total cost curve as output increases are just flip-sidesof the same phenomenon. That is, as output increases, the marginal cost of output alsoincreases because the marginal product of the variable input decreases. Our next step isto introduce another measure of cost: average cost.

Average CostIn addition to total cost and marginal cost, it’s useful to calculate average total cost,often simply called average cost. The average total cost is total cost divided by thequantity of output produced; that is, it is equal to total cost per unit of output. If we letATC denote average total cost, the equation looks like this:

(55-3) ATC = =

Average total cost is important because it tells the producer how much the average ortypical unit of output costs to produce. Marginal cost, meanwhile, tells the producerhow much one more unit of output costs to produce. Although they may look very sim-ilar, these two measures of cost typically differ. And confusion between them is a majorsource of error in economics, both in the classroom and in real life. Table 55.2 uses datafrom Selena’s Gourmet Salsas to calculate average total cost. For example, the totalcost of producing 4 cases of salsa is $300, consisting of $108 in fixed cost and $192 invariable cost (from Table 55.1). So the average total cost of producing 4 cases of salsa is

Total costQuantity of output

TCQ


Average Costs for Selena’s Gourmet Salsas

Quantityof salsa Total Average total Average fixed Average variable

Q cost cost of case cost of case cost of case(cases) TC ATC = TC /Q AFC = FC /Q AVC = VC /Q

1 $120 $120.00 $108.00 $12.00

2 156 78.00 54.00 24.00

3 216 72.00 36.00 36.00

4 300 75.00 27.00 48.00

5 408 81.60 21.60 60.00

6 540 90.00 18.00 72.00

7 696 99.43 15.43 84.00

8 876 109.50 13.50 96.00

9 1,080 120.00 12.00 108.00

10 1,308 130.80 10.80 120.00

t a b l e 55.2

Average total cost, often referred to simply

as average cost, is total cost divided by

quantity of output produced.


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$300/4 = $75. You can see from Table 55.2 that as the quantity of output increases, av-erage total cost first falls, then rises.

Figure 55.3 plots that data to yield the average total cost curve, which shows how aver-age total cost depends on output. As before, cost in dollars is measured on the verticalaxis and quantity of output is measured on the horizontal axis. The average total costcurve has a distinctive U shape that corresponds to how average total cost first fallsand then rises as output increases. Economists believe that such U-shaped averagetotal cost curves are the norm for firms in many industries.

f i g u r e 55.3

Average Total Cost Curve forSelena’s Gourmet SalsasThe average total cost curve at Selena’s Gour-met Salsas is U-shaped. At low levels of out-put, average total cost falls because the“spreading effect” of falling average fixed costdominates the “diminishing returns effect” ofrising average variable cost. At higher levels ofoutput, the opposite is true and average totalcost rises. At point M, corresponding to an out-put of three cases of salsa per day, averagetotal cost is at its minimum level, the minimumaverage total cost.

Average total cost, ATC

M

7 8 9 106543210

$140

120

100

80

60

40

20

Cost ofcase

Quantity of salsa (cases)

Minimumaveragetotal cost

Minimum-cost output

To help our understanding of why the average total cost curve is U-shaped, Table55.2 breaks average total cost into its two underlying components, average fixed cost andaverage variable cost. Average fixed cost, or AFC, is fixed cost divided by the quantity ofoutput, also known as the fixed cost per unit of output. For example, if Selena’s Gour-met Salsas produces 4 cases of salsa, average fixed cost is $108/4 = $27 per case. Aver-age variable cost, or AVC, is variable cost divided by the quantity of output, alsoknown as variable cost per unit of output. At an output of 4 cases, average variable costis $192/4 = $48 per case. Writing these in the form of equations:

(55-4) AFC = =

AVC = =

Average total cost is the sum of average fixed cost and average variable cost; it has a Ushape because these components move in opposite directions as output rises.

Average fixed cost falls as more output is produced because the numerator (thefixed cost) is a fixed number but the denominator (the quantity of output) increases asmore is produced. Another way to think about this relationship is that, as more outputis produced, the fixed cost is spread over more units of output; the end result is that the

Variable costQuantity of output

VCQ

Fixed costQuantity of output

FCQ

A U-shaped average total cost

curve falls at low levels of output and

then rises at higher levels.

Average fixed cost is the fixed cost per

unit of output.

Average variable cost is the variable cost

per unit of output.

fixed cost per unit of output—the average fixed cost—falls. You can see this effect in thefourth column of Table 55.2: average fixed cost drops continuously as output in-creases. Average variable cost, however, rises as output increases. As we’ve seen, this re-flects diminishing returns to the variable input: each additional unit of output addsmore to variable cost than the previous unit because increasing amounts of the variableinput are required to make another unit.

So increasing output has two opposing effects on average total cost—the “spreadingeffect” and the “diminishing returns effect”:■ The spreading effect. The larger the output, the greater the quantity of output over

which fixed cost is spread, leading to lower average fixed cost.■ The diminishing returns effect. The larger the output, the greater the amount of variable

input required to produce additional units, leading to higher average variable cost.

At low levels of output, the spreading effect is very powerful because even small in-creases in output cause large reductions in average fixed cost. So at low levels of out-put, the spreading effect dominates the diminishing returns effect and causes theaverage total cost curve to slope downward. But when output is large, average fixed costis already quite small, so increasing output further has only a very small spreading ef-fect. Diminishing returns, however, usually grow increasingly important as outputrises. As a result, when output is large, the diminishing returns effect dominates thespreading effect, causing the average total cost curve to slope upward. At the bottom ofthe U-shaped average total cost curve, point M in Figure 55.3, the two effects exactlybalance each other. At this point average total cost is at its minimum level, the mini-mum average total cost.

Figure 55.4 brings together in a single picture the four other cost curves that wehave derived from the total cost curve for Selena’s Gourmet Salsas: the marginal costcurve (MC ), the average total cost curve (ATC ), the average variable cost curve (AVC ),and the average fixed cost curve (AFC ). All are based on the information in Tables 55.1and 55.2. As before, cost is measured on the vertical axis and the quantity of output ismeasured on the horizontal axis.


Phot

odis

c

f i g u r e 55.4

Marginal Cost and AverageCost Curves for Selena’sGourmet SalsasHere we have the family of cost curves for Se-lena’s Gourmet Salsas: the marginal cost curve(MC ), the average total cost curve (ATC ), theaverage variable cost curve (AVC ), and the av-erage fixed cost curve (AFC ). Note that the av-erage total cost curve is U-shaped and themarginal cost curve crosses the average totalcost curve at the bottom of the U, point M, cor-responding to the minimum average total costfrom Table 55.2 and Figure 55.3.

$250

200

150

100

50

Cost ofcase


M

Minimum-cost output

0

MC

ATCAVC

AFC

Let’s take a moment to note some features of the various cost curves. First of all,marginal cost slopes upward—the result of diminishing returns that make an addi-tional unit of output more costly to produce than the one before. Average variable costalso slopes upward—again, due to diminishing returns—but is flatter than the mar-ginal cost curve. This is because the higher cost of an additional unit of output is aver-aged across all units, not just the additional unit, in the average variable cost measure.Meanwhile, average fixed cost slopes downward because of the spreading effect.

Finally, notice that the marginal cost curve intersects the average total cost curvefrom below, crossing it at its lowest point, point M in Figure 55.4. This last feature isour next subject of study.

Minimum Average Total CostFor a U-shaped average total cost curve, average total cost is at its minimum level at thebottom of the U. Economists call the quantity of output that corresponds to the mini-mum average total cost the minimum-cost output. In the case of Selena’s GourmetSalsas, the minimum-cost output is three cases of salsa per day.

In Figure 55.4, the bottom of the U is at the level of output at which the marginalcost curve crosses the average total cost curve from below. Is this an accident? No—it re-flects general principles that are always true about a firm’s marginal cost and averagetotal cost curves:■ At the minimum-cost output, average total cost is equal to marginal cost.■ At output less than the minimum-cost output, marginal cost is less than average total

cost and average total cost is falling.■ And at output greater than the minimum-cost output, marginal cost is greater than

average total cost and average total cost is rising.

To understand these principles, think about how your grade in one course—say, a3.0 in physics—affects your overall grade point average. If your GPA before receivingthat grade was more than 3.0, the new grade lowers your average.

Similarly, if marginal cost—the cost of producing one more unit—is less than aver-age total cost, producing that extra unit lowers average total cost. This is shown in Fig-ure 55.5 by the movement from A1 to A2. In this case, the marginal cost of producing


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f i g u r e 55.5

The Relationship Between theAverage Total Cost and theMarginal Cost CurvesTo see why the marginal cost curve (MC ) mustcut through the average total cost curve at theminimum average total cost (point M ), corre-sponding to the minimum-cost output, we lookat what happens if marginal cost is differentfrom average total cost. If marginal cost is lessthan average total cost, an increase in outputmust reduce average total cost, as in the move-ment from A1 to A2. If marginal cost is greaterthan average total cost, an increase in outputmust increase average total cost, as in themovement from B1 to B2.

Cost ofunit

Quantity

MC

ATC

MCL

MCH

A1

B1A2

B2

M

If marginal cost isbelow average totalcost, average totalcost is falling.

If marginal cost isabove average totalcost, average totalcost is rising.

The minimum-cost output is the

quantity of output at which average

total cost is lowest—it corresponds to the

bottom of the U-shaped average total cost

curve.

an additional unit of output is low, as indicated by the point MCL on the marginal costcurve. When the cost of producing the next unit of output is less than average totalcost, increasing production reduces average total cost. So any quantity of output atwhich marginal cost is less than average total cost must be on the downward-slopingsegment of the U.

But if your grade in physics is more than the average of your previous grades, thisnew grade raises your GPA. Similarly, if marginal cost is greater than average total cost,producing that extra unit raises average total cost. This is illustrated by the movementfrom B1 to B2 in Figure 55.5, where the marginal cost, MCH , is higher than average totalcost. So any quantity of output at which marginal cost is greater than average total costmust be on the upward-sloping segment of the U.

Finally, if a new grade is exactly equal to your previous GPA, the additional gradeneither raises nor lowers that average—it stays the same. This corresponds to point M inFigure 55.5: when marginal cost equals average total cost, we must be at the bottom ofthe U because only at that point is average total cost neither falling nor rising.

Does the Marginal Cost Curve Always Slope Upward?Up to this point, we have emphasized the importance of diminishing returns, whichlead to a marginal product curve that always slopes downward and a marginal costcurve that always slopes upward. In practice, however, economists believe that mar-ginal cost curves often slope downward as a firm increases its production from zero upto some low level, sloping upward only at higher levels of production: marginal costcurves look like the curve labeled MC in Figure 55.6.

This initial downward slope occurs because a firm often finds that, when it startswith only a very small number of workers, employing more workers and expandingoutput allows its workers to specialize in various tasks. This, in turn, lowers the firm’smarginal cost as it expands output. For example, one individual producing salsa wouldhave to perform all the tasks involved: selecting and preparing the ingredients, mixingthe salsa, bottling and labeling it, packing it into cases, and so on. As more workers areemployed, they can divide the tasks, with each worker specializing in one or a few as-pects of salsa-making. This specialization leads to increasing returns to the hiring of ad-ditional workers and results in a marginal cost curve that initially slopes downward.


f i g u r e 55.6

More Realistic Cost CurvesA realistic marginal cost curve has a “swoosh”shape. Starting from a very low output level,marginal cost often falls as the firm increasesoutput. That’s because hiring additional workersallows greater specialization of their tasks andleads to increasing returns. Once specializationis achieved, however, diminishing returns to ad-ditional workers set in and marginal cost rises.The corresponding average variable cost curveis now U-shaped, like the average total costcurve.

Costof unit

Quantity

MCATC

AVC

2. . . . but diminishing returnsset in once the benefits fromspecialization are exhaustedand marginal cost rises.

1. Increasing specialization leadsto lower marginal cost, . . .

M o d u l e 55 AP R e v i e w

Check Your Understanding 1. Alicia’s Apple Pies is a roadside business. Alicia must pay $9.00

in rent each day. In addition, it costs her $1.00 to produce thefirst pie of the day, and each subsequent pie costs 50% more toproduce than the one before. For example, the second pie costs$1.00 × 1.5 = $1.50 to produce, and so on.a. Calculate Alicia’s marginal cost, variable cost, average fixed

cost, average variable cost, and average total cost as her dailypie output rises from 0 to 6. (Hint: The variable cost of twopies is just the marginal cost of the first pie, plus themarginal cost of the second, and so on.)

b. Indicate the range of pies for which the spreading effectdominates and the range for which the diminishing returnseffect dominates.

c. What is Alicia’s minimum-cost output? Explain why making one more pie lowers Alicia’s average total cost when output is lower than the minimum-cost output.Similarly, explain why making one more pie raises Alicia’s average total cost when output is greater than theminimum-cost output.

Solutions appear at the back of the book.


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But once there are enough workers to have completely exhausted the benefits of fur-ther specialization, diminishing returns to labor set in and the marginal cost curvechanges direction and slopes upward. So typical marginal cost curves actually have the“swoosh” shape shown by MC in Figure 55.6. For the same reason, average variable costcurves typically look like AVC in Figure 55.6: they are U-shaped rather than strictly up-ward sloping.

However, as Figure 55.6 also shows, the key features we saw from the example of Se-lena’s Gourmet Salsas remain true: the average total cost curve is U-shaped, and themarginal cost curve passes through the point of minimum average total cost.

Tackle the Test: Multiple-Choice Questions1. When a firm is producing zero output, total cost equals

a. zero.b. variable cost.c. fixed cost.d. average total cost.e. marginal cost.

2. Which of the following statements is true?I. Marginal cost is the change in total cost generated by one

additional unit of output.II. Marginal cost is the change in variable cost generated by

one additional unit of output.III. The marginal cost curve must cross the minimum of the

average total cost curve.a. I onlyb. II onlyc. III onlyd. I and II onlye. I, II, and III

3. Which of the following is correct?a. AVC is the change in total cost generated by one additional

unit of output.b. MC = TC/Qc. The average cost curve crosses at the minimum of the

marginal cost curve.

d. The AFC curve slopes upward.e. AVC = ATC − AFC

4. The slope of the total cost curve equalsa. variable cost.b. average variable cost.c. average total cost.d. average fixed cost.e. marginal cost.

5. Q VC TC0 $0 $401 20 602 50 903 90 1304 140 1805 200 240

On the basis of the data in the table above, what is the marginalcost of the third unit of output?a. 40b. 50c. 60d. 90e. 130

what you will learn module: module 55 firm...

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